subdivide at line at the selected location (vertex) of that line?
Here is how I accomplish this when I am modeling:

First, select the edge you want the vertex to be added to.  Then hit W > subdivide.  This will add a new vertex on the edge, then select both the new vertex and then the original one (making sure to select them in that order) and hit Alt + M > at last.  This will merge the two vertices to the location where the original vertex was.